As interactive mediums such as the Internet and teleconferencing gain popularity, demands on data transmission bandwidth also grow. The growth is currently so explosive that demand may soon exceed capacity. When demand outstrips capacity, data transmission is slowed and transmissions are more prone to error. Obvious solutions include increasing bandwidth capacity or, alternatively, reducing bandwidth demand. Updating existing transmission lines and installing new switching equipment, as a means for increasing capacity, is both costly and time consuming. Reducing bandwidth demand can be inexpensively accomplished by better compression techniques. Compression techniques reduce transmission bandwidth requirements by transmitting fewer bits. The effect of transmitting fewer bits is reduced transmission time and an opportunity to transmit more information in less time.
One problem with state of the art compression and processing technology is manifested in applications where hardware size and processing speed are significant issues, as is the case with many small-scale portable circuits. In such situations, size and speed are critical criteria. Striking the right balance between size and speed is further complicated by the need to limit power consumption. Failure to properly balance these parameters will result in a sub-optimal system. State of the art systems have inseparably coupled speed with circuit complexity, and circuit complexity with size, cost, and power requirements. Since portable units are generally dependent on portable power sources, power consumption must be minimized or the advantages achieved through reductions in apparatus size will be lost with the attachment of oversized power supplies. Furthermore, power consumption generates heat, which can have both long and short-term deleterious effects on micro-circuitry.
The need for more effective and efficient data transformation and processing techniques is ongoing, but such improvements must not be performed at the cost of data quality. The post transformation data needs to be both present and distinguishable from noise or other spurious signals. Many of the issues discussed in the foregoing are not unique to data compression but apply to the field of data manipulation and processing as a whole. For instance, optimizing computational complexity and power consumption are desirable in most data processing systems. Thus, artisans are faced with competing goals. First: optimally sparsening data, so as to minimize processing, transmission, and storage requirements without losing critical data, and second: performing the first goal in a manner that is neither too costly nor so complex that slow hardware obviates the advantages of the data sparsening.
A growing body of literature exists regarding wavelet transformation technology concerning both theoretical and practical applications, as surveyed by the following articles, which are herein incorporated by reference:    S. Mallat, “Multifrequency Channel Decompositions of Images and Wavelet Models,” IEEE Trans. Acoustics, Speech and Signal Processing, vol. 3 No. 12 December 1989.    S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 11 No. 7, July 1989.    Vetterli et al., “Wavelets and Filter Banks: Theory and Design”, IEEE Transactions on Signal Processing, vol. 40, No. 9, September 1992.    Rioul et al., “Fast Algorithms for Discrete and Continuous Wavelet Transforms”, IEEE Transactions on Information Theory, vol. 38, No. 2, March 1992.    M. J. Shensa, “Discrete Wavelet Transforms: The Relationship of the a Trous and Mallat Algorithms”, Trezieme Colloque Sur Le Traitement Di Signal et des Images, 16 Sep. 1991.    Flandrin et al., “Generalized Target Description and Wavelet Decomposition”, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, No. 2, February 1990.